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A made-up teacher records the hours of revision and the test marks of eleven students…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A made-up teacher records the hours of revision and the test marks of eleven students. The hours are $0$ to $10$ , one student for each whole number of hours. The marks, in that order, are $35$ , $42$ , $40$ , $51$ , $55$ , $58$ , $62$ , $61$ , $67$ , $64$ and $70$ . Find $r$ for all eleven students. Then find $r$ only for the five students who revised for $6$ to $10$ hours. Give both to four decimal places, and explain the difference.

Need a reminder? The key ideaShow

$r$ measures straight-line patterns only. A curve can give $r$ near $0$ , one outlier can change $r$ a lot, and a narrow range of $x$ usually lowers $r$ . Changing units, or adding a number, leaves $r$ alone; multiplying by a negative number changes its sign.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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